Mathematics Colloquium

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The soliton resolution conjecture for equivariant wave maps

Speaker: Andrew Lawrie, MIT

Location: Online

Videoconference link: https://nyu.zoom.us/rec/share/2Gmv5-5fQYBoFnyxV71YMVbkPN7L0tMmmrPX8v6OUYP-WKpTB0rRxPl1Z8WzZXpK.p5eD10TtLrCahiWC

Date: Monday, October 18, 2021, 3:45 p.m.

Synopsis:

 I will present a joint work with Jacek Jendrej (CRNS, Sorbonne Paris Nord) on equivariant wave maps with values in the two-sphere. We prove that every finite energy solution resolves, as time passes, into a superposition of harmonic maps (solitons) and radiation. It was proved in works of Côte, and Jia and Kenig, that such a decomposition holds along a sequence of times. We show the resolution holds continuously-in-time via a dynamical “no-return” analysis based on the virial identity. The proof combines a modulation analysis of solutions near a multi-soliton configuration with concentration compactness techniques.